Analysing a pie chart is really about analysing the data; the pie chart itself is actually the visual analysis of data. So, in reality, you analyse the data then create the pie chart as a representation of your analysis. If, however, as a student, you've been given a drawn pie chart without data analysis on it, then you can reverse the process and look at the chart and calculate backwards for the data analysis. For this you'll need a protractor and will have to do some simple maths calculations.
Look at the pie chart for your initial analysis. The larger the section the more important or greater value that piece represents. Your chart is probably labelled with what the slice represents. For example, say the chart represents the types of horses you have at your farm. So one slice is for pintos, another for palominos, one for thoroughbreds, and so forth. Each slice represents what per cent of the herd is that type of horse.
Measure the interior angle of a slice with the protractor. Start with the biggest slice. Work your way around the chart, measuring every angle of every slice. In the end, all the angles together should add up to 360 degrees. If they don't, remeasure.
Convert the angle to what fraction of the circle it represents. Take each of your angle measurements and place them over 360. For example, if one slice was 90 degrees, you would create the fraction 90/360. Now the fraction. 90/360 reduces to 1/4. Do this for each section of the pie chart.
Convert the fractions to percentages. For this, all you have to do is divide and multiply by 100. If you don't like working with decimals, you can multiply first (as the operations have the same hierarchy.) So, to convert 1/4 to a percentage, you can multiply by 100 getting 100/4 then doing the division. 4 divides into 100 exactly 25 times. Your answer is 25 per cent; that is, that slice of the pie chart represents 25 per cent. So if that was your per cent of pintos, then pintos comprise 25 per cent of your total herd. Do the same analysis for all slices.